This chapter announces our upcoming result on k-Yamabe solitons. These are special solutions to a fully non-linear geometric flow that extends the well-known Yamabe flow. The equation that we are proposing has only been understood in some special cases (specific choices of parameters and compact locally conformally flat manifolds) and the study of solitons is relevant to extend this understanding, particularly in describing possible singularities that may form during the evolution. Our contribution is a first step in that direction.